TSTP Solution File: SET884+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET884+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:10:30 EDT 2023
% Result : Theorem 1.96s 1.15s
% Output : CNFRefutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 14 unt; 0 def)
% Number of atoms : 187 ( 110 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 234 ( 91 ~; 85 |; 47 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 99 ( 0 sgn; 72 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,conjecture,
! [X0,X1,X2] :
~ ( X0 != X2
& X0 != X1
& subset(singleton(X0),unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( X0 != X2
& X0 != X1
& subset(singleton(X0),unordered_pair(X1,X2)) ),
inference(negated_conjecture,[],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f14,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f15,plain,
? [X0,X1,X2] :
( X0 != X2
& X0 != X1
& subset(singleton(X0),unordered_pair(X1,X2)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f16,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f17,f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) )
=> ( ( ( sK1(X0,X1,X2) != X1
& sK1(X0,X1,X2) != X0 )
| ~ in(sK1(X0,X1,X2),X2) )
& ( sK1(X0,X1,X2) = X1
| sK1(X0,X1,X2) = X0
| in(sK1(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ( ( ( sK1(X0,X1,X2) != X1
& sK1(X0,X1,X2) != X0 )
| ~ in(sK1(X0,X1,X2),X2) )
& ( sK1(X0,X1,X2) = X1
| sK1(X0,X1,X2) = X0
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f22,f23]) ).
fof(f29,plain,
( ? [X0,X1,X2] :
( X0 != X2
& X0 != X1
& subset(singleton(X0),unordered_pair(X1,X2)) )
=> ( sK4 != sK6
& sK4 != sK5
& subset(singleton(sK4),unordered_pair(sK5,sK6)) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
( sK4 != sK6
& sK4 != sK5
& subset(singleton(sK4),unordered_pair(sK5,sK6)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f15,f29]) ).
fof(f32,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f34,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
! [X2,X0,X1,X4] :
( X1 = X4
| X0 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
! [X2,X0,X1] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f47,plain,
subset(singleton(sK4),unordered_pair(sK5,sK6)),
inference(cnf_transformation,[],[f30]) ).
fof(f48,plain,
sK4 != sK5,
inference(cnf_transformation,[],[f30]) ).
fof(f49,plain,
sK4 != sK6,
inference(cnf_transformation,[],[f30]) ).
fof(f50,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f34]) ).
fof(f51,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f50]) ).
fof(f57,plain,
! [X0,X1,X4] :
( X1 = X4
| X0 = X4
| ~ in(X4,unordered_pair(X0,X1)) ),
inference(equality_resolution,[],[f37]) ).
cnf(c_50,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f32]) ).
cnf(c_53,plain,
in(X0,singleton(X0)),
inference(cnf_transformation,[],[f51]) ).
cnf(c_60,plain,
( ~ in(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_61,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f43]) ).
cnf(c_65,negated_conjecture,
sK4 != sK6,
inference(cnf_transformation,[],[f49]) ).
cnf(c_66,negated_conjecture,
sK4 != sK5,
inference(cnf_transformation,[],[f48]) ).
cnf(c_67,negated_conjecture,
subset(singleton(sK4),unordered_pair(sK5,sK6)),
inference(cnf_transformation,[],[f47]) ).
cnf(c_69,plain,
in(sK4,singleton(sK4)),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_151,plain,
subset(singleton(sK4),unordered_pair(sK6,sK5)),
inference(demodulation,[status(thm)],[c_67,c_50]) ).
cnf(c_217,plain,
( unordered_pair(sK6,sK5) != X1
| singleton(sK4) != X0
| ~ in(X2,X0)
| in(X2,X1) ),
inference(resolution_lifted,[status(thm)],[c_61,c_151]) ).
cnf(c_218,plain,
( ~ in(X0,singleton(sK4))
| in(X0,unordered_pair(sK6,sK5)) ),
inference(unflattening,[status(thm)],[c_217]) ).
cnf(c_569,plain,
( ~ in(X0,singleton(sK4))
| X0 = sK6
| X0 = sK5 ),
inference(superposition,[status(thm)],[c_218,c_60]) ).
cnf(c_575,plain,
( ~ in(sK4,singleton(sK4))
| sK4 = sK6
| sK4 = sK5 ),
inference(instantiation,[status(thm)],[c_569]) ).
cnf(c_576,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_575,c_65,c_66,c_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET884+1 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 16:06:04 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.96/1.15 % SZS status Started for theBenchmark.p
% 1.96/1.15 % SZS status Theorem for theBenchmark.p
% 1.96/1.15
% 1.96/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.96/1.15
% 1.96/1.15 ------ iProver source info
% 1.96/1.15
% 1.96/1.15 git: date: 2023-05-31 18:12:56 +0000
% 1.96/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.96/1.15 git: non_committed_changes: false
% 1.96/1.15 git: last_make_outside_of_git: false
% 1.96/1.15
% 1.96/1.15 ------ Parsing...
% 1.96/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.96/1.15
% 1.96/1.15 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e
% 1.96/1.15
% 1.96/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.96/1.15
% 1.96/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.96/1.15 ------ Proving...
% 1.96/1.15 ------ Problem Properties
% 1.96/1.15
% 1.96/1.15
% 1.96/1.15 clauses 16
% 1.96/1.15 conjectures 2
% 1.96/1.15 EPR 4
% 1.96/1.15 Horn 13
% 1.96/1.15 unary 7
% 1.96/1.15 binary 3
% 1.96/1.15 lits 32
% 1.96/1.15 lits eq 18
% 1.96/1.15 fd_pure 0
% 1.96/1.15 fd_pseudo 0
% 1.96/1.15 fd_cond 0
% 1.96/1.15 fd_pseudo_cond 5
% 1.96/1.15 AC symbols 0
% 1.96/1.15
% 1.96/1.15 ------ Schedule dynamic 5 is on
% 1.96/1.15
% 1.96/1.15 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.96/1.15
% 1.96/1.15
% 1.96/1.15 ------
% 1.96/1.15 Current options:
% 1.96/1.15 ------
% 1.96/1.15
% 1.96/1.15
% 1.96/1.15
% 1.96/1.15
% 1.96/1.15 ------ Proving...
% 1.96/1.15
% 1.96/1.15
% 1.96/1.15 % SZS status Theorem for theBenchmark.p
% 1.96/1.15
% 1.96/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.96/1.15
% 1.96/1.15
%------------------------------------------------------------------------------